Kenya’s interior minister says three Islamic militants are dead and officials are “very certain” there are few -- if any -- hostages left inside a Nairobi mall after military forces led a new rescue operation to end the terror attack Monday.

Sources tell Fox News that Kenyan security forces exchanged fire with what was believed to be 10 to 15 gunmen hiding on the top floor of the building for several hours Monday morning, neutralizing most of them. Kenya’s chief of defense forces says troops are in control of all floors inside the mall -- though he says terrorists could still be hiding inside.

Interior Minister Joseph Ole Lenku told the press that three militants died and more hostages were freed in the efforts to end the ongoing siege waged since Saturday by al-Shabab, a Somali group with ties to Al Qaeda. Lenku says the evacuation of hostages has gone "very, very well” and that Kenyan officials are "very certain" that there are few if any hostages left in the building. The government has never said how many hostages they believe were being held.

Officials say at least 62 people were killed and 200 wounded in the weekend attack, while 63 were reported missing.

Four booming blasts shook the building Monday morning, sending plumes of thick smoke into the sky. The gunmen holed up inside the mall had caused the smoke by setting mattresses on fire in a supermarket as a decoy, according to a Reuters report.

Three attackers were killed in the fighting Monday, officials said, and more than 10 suspects arrested. Eleven Kenyan soldiers were wounded in the running gun battles. By evening, Kenyan security officials were claiming the upper hand.

"Taken control of all the floors. We're not here to feed the attackers with pastries but to finish and punish them," Police Inspector General David Kimaiyo said on Twitter.

From neighboring Somalia, al-Shabab spokesman Sheik Ali Mohamud Rage said in a recorded message posted on a website that the terrorists had been ordered to "take punitive action against the hostages" if force was used to try to rescue them.

"Israelis and Kenyan forces have tried to enter Westgate by force but they could not," Rage reportedly said in the audio statement. "The mujahadeen will kill the hostages if the enemies use force."

Kenya Chief of Defense Forces Gen. Julius Karangi said he believes the attackers are from many countries. "We have an idea who these people are and they are clearly a multinational collection from all over the world," he said.

At the Oshwal Centre next to the mall, the Red Cross was using a squat concrete structure that houses a Hindu temple as a triage center. Medical workers attended to at least two wounded Kenyan soldiers there Monday.

President Obama said the U.S. was providing all the cooperation possible to Kenya. “I want to express personally not only my condolences to President Kenyatta who lost two family members in the attack, but to the Kenyan people.We stand with them against this terrible outrage that’s occurred. We will provide them with whatever law enforcement support that is necessary,” Obama said during a meeting with Nigerian President Goodluck Jonathan in New York Monday.

Meanwhile, the FBI and U.S intelligence officials are "aggressively" investigating whether or not Americans were among the militants who attacked the mall, a federal law enforcement source told Fox News.

FBI officials told Fox they cannot yet confirm or deny whether any of the assailants are or were Americans. "We just don't know yet. We're still trying to figure it out," said the source.

The FBI does have agents on the ground in Nairobi. "We have people there 365 days of the year and they are monitoring the situation and are in touch with local authorities who have the lead on this."

"All we've seen are the same reports coming out of Al Shabab ... but we have to run those to ground,'' White House deputy national security adviser Ben Rhodes told reporters Monday.

"We do monitor very carefully and have for some time been concerned about, efforts by al-Shabaab to recruit Americans or U.S. persons to come to Somalia,'' Rhodes said while traveling with the president to the United Nations.

The military assault began shortly before sundown on Saturday at the upscale mall. Kenya's presidential office said that one of the attackers was arrested on Saturday and died after suffering from bullet wounds.

Many of the rescued hostages -- mostly adults -- were suffering from dehydration, Col. Cyrus Oguna, a military spokesman, told The Associated Press.

Cecile Ndwiga said she had been hiding under a car in the basement parking garage.

"I called my husband to ask the soldiers to come and rescue me. Because I couldn't just walk out anyhow. The shootout was all over here -- left, right -- just gunshots," she said.

Kenyan President Uhuru Kenyatta said in an address that the attackers "shall not get away with their despicable and beastly acts." "We will punish the masterminds swiftly and indeed very painfully," he added.

White House officials said Sunday that President Obama called Kenyatta to tell him the United States supports the country's effort to bring al-Shabab to justice.

Kenyans and foreigners were among those confirmed dead, including French, Canadians and Chinese. The U.S. State Department said four American citizens were injured and were being given assistance. The victims ranged in age from 2 to 78, Reuters reports.

Nineteen people, including at least four children, died after being admitted to Nairobi's MP Shah hospital, said Manoj Shah, the hospital's chairman. Kenyatta's nephew and the nephew's fiancée are also among the dead.

The al-Shabab extremist Islamic terrorist force grew out of the anarchy that crippled Somalia after warlords ousted a longtime dictator in 1991. Its name means "The Youth" in Arabic, and it was a splinter youth wing of a weak Islamic Courts Union government created in 2006 to establish a fundamentalist Islamic state in the East African nation.

Al-Shabab is estimated to have several thousand fighters, including a few hundred foreign fighters. Some of the insurgents' foreign fighters are from the Middle East with experience in the Iraq and Afghanistan conflicts. Others are young, raw recruits from Somali communities in the United States and Europe.